Basic Math Examples

$\frac{(z^{2} - 4) \cdot 1}{2 - z}$

Step 1

Multiply $z^{2} - 4$ by $1$ .

$\frac{z^{2} - 4}{2 - z}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{z^{2} - 2^{2}}{2 - z}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = z$ and $b = 2$ .

$\frac{(z + 2) (z - 2)}{2 - z}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $z - 2$ and $2 - z$ .

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Step 3.1.1

Factor $- 1$ out of $z$ .

$\frac{(z + 2) (- 1 (- z) - 2)}{2 - z}$

Step 3.1.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{(z + 2) (- 1 (- z) - 1 (2))}{2 - z}$

Step 3.1.3

Factor $- 1$ out of $- 1 (- z) - 1 (2)$ .

$\frac{(z + 2) (- 1 (- z + 2))}{2 - z}$

Step 3.1.4

Reorder terms.

$\frac{(z + 2) (- 1 (- z + 2))}{- z + 2}$

Step 3.1.5

Cancel the common factor.

$\frac{(z + 2) (- 1 (- z + 2))}{- z + 2}$

Step 3.1.6

Divide $(z + 2) \cdot (- 1)$ by $1$ .

$(z + 2) \cdot (- 1)$

Step 3.2

Simplify by multiplying through.

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Step 3.2.1

Apply the distributive property.

$z \cdot - 1 + 2 \cdot - 1$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Move $- 1$ to the left of $z$ .

$- 1 \cdot z + 2 \cdot - 1$

Step 3.2.2.2

Multiply $2$ by $- 1$ .

$- 1 \cdot z - 2$

Step 3.3

Rewrite $- 1 z$ as $- z$ .

$- z - 2$